In this paper, we examine the prefetching strategies in a peer-driven video on-demand system. In our design, each video is encoded into multiple low bit-rate substreams and copies of the substreams are distributed to the participating peers. When a peer streams in a substream of rate r, it instead streams at rate r̂ where r̂ > r. In this manner, if one of the peer's suppliers disconnects, the client peer can tap the reservoir of prefetched bits while searching for a replacement server, thereby avoiding any glitches or reduced visual quality. We examine how to assign prefetching rates to each of substreams as a function of their importance. Our studies show that appropriate prefetching strategies can bring significant performance improvements for both multiple description and layered videos.